Factorise 4a+4b with procedure
Answers
Step-by-step explanation:
4a+4b=0
4(a+b)=0
a=-b
Answer:
STEP
1
:
b
Simplify —
a
Equation at the end of step
1
:
b
(4a - (4 • —)) - b
a
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using a as the denominator :
4a 4a • a
4a = —— = ——————
1 a
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
4a • a - (4b) 4a2 - 4b
————————————— = ————————
a a
Equation at the end of step
2
:
(4a2 - 4b)
—————————— - b
a
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using a as the denominator :
b b • a
b = — = —————
1 a
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
4a2 - 4b = 4 • (a2 - b)
Trying to factor as a Difference of Squares:
4.2 Factoring: a2 - b
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : a2 is the square of a1
Check : b1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
4 • (a2-b) - (b • a) 4a2 - ab - 4b
———————————————————— = —————————————
a a
Trying to factor a multi variable polynomial :
4.4 Factoring 4a2 - ab - 4b
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
4a2 - ab - 4b
—————————————
a
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